Integrability in [d+1] dimensions: combined local equations and commutativity of the transfer matrices

We propose new inhomogeneous local integrability equations–combined equations, for statistical vertex models of general dimensions in the framework of the Algebraic Bethe Ansatz (ABA). For the low-dimensional cases the efficiency of the step-by-step consideration of the transfer matrices’ commutatio...

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Bibliographic Details
Published in:European physical journal plus 2023-11, Vol.138 (11), p.1058, Article 1058
Main Author: Khachatryan, Shahane A.
Format: Article
Language:English
Subjects:
Algebra
Applied and Technical Physics
Atomic
Commutativity
Complex Systems
Condensed Matter Physics
Integral equations
Mathematical and Computational Physics
Molecular
Optical and Plasma Physics
Physics
Physics and Astronomy
Qubits (quantum computing)
Regular Article
Spacetime
Symmetry
Theoretical
Transfer matrices
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Summary:We propose new inhomogeneous local integrability equations–combined equations, for statistical vertex models of general dimensions in the framework of the Algebraic Bethe Ansatz (ABA). For the low-dimensional cases the efficiency of the step-by-step consideration of the transfer matrices’ commutation is demonstrated. We construct some simple 3D solutions with the three-state R -matrices of certain 20-vertex structure; the connection with the quantum three-qubit gates is discussed. New, restricted versions of 3D local integrability equations with four-state R -matrices are defined, too. Then we construct a new 3D analog of the two-dimensional star-triangle equations.
ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/s13360-023-04711-w